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Stabilizer-free polygonal and polyhedral virtual elements
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DOI：10.1016/j.apnum.2025.10.015.png)
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Abstract
En 中文
Stabilizer-free Pk virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous Pk polynomials on a triangular-subdivision of each polygon, or a tetrahedral-subdivision of each polyhedron. With such an accurate and proper interpolation, the stabilizer of the virtual elements is eliminated while the system is kept positive-definite. We show that the stabilizer-free virtual elements converge at the optimal order in 2D and 3D. Numerical examples are computed, validating the theory.
Keywords:
Virtual element
Stabilizer-free
Elliptic equation
Polygonal mesh
Polyhedral mesh
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